... Got it. I installed the latest PCMCIA (3.1.10) on my Satelite 4030 CDT. The OS is Caldera Open Linux 2.3 (free version from magazine CHIP).
I tried a lot with BIOS defaults (Mode Automatic), but that didn't work. I had to switch to 'Cardbus/16'. After that the Card came up and works now. Here my addition to pcmcia/config: